Coconut trees produce "up to" 75 fruits per year, according to the wikipedia article.

A "cartoon" island with a single palm and about the same square footage as an average bedroom during high tide is better than a raft in some ways I suppose... but not much. You won't get seasick and probably won't have salt sores from staying in one spot too long immersed in salt water... but it also means you're not going anywhere! You'd still need to live off the sea, not so much off the island.

Depending on where the island is located, you could get plenty of fresh water from rain, or it may not rain for weeks....